What is the value of the expression (81 1/4) ^4

Recall that to determine if a table represents a probability distribution, the sum of the probabilities must add up to 1, and all the probabilities have to be positive numbers less or equal to 1.

Now, notice that:

From the table, we notice that all the given probabilities are positive numbers between 0 and 1. Therefore, we can conclude that the given table represents a probability distribution.

Yes, it is a probability distribution.

Answer:

23 is the answer u understand

Answer:

x= 18

10x=180

x=180/10

x=18

Answer:

The process capability index for this system is 0.9103

Step-by-step explanation:

Upper specification = 1.649 inches

Lowe Specification = 1.507 inches

Mean = 1.57 inches

Standard Deviation = 0.026 inches

Process Capability Index = PCI

PCI = (Upper specification - lower specification)/6(standard deviation)

So, we get,

PCI = (1.649 - 1.507)/((6)(0.026))

PCI = 0.142/0.156

PCI = 0.9102564

To four decimal places, we get,

PCI = 0.9103

The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

y" = sec(x) · [sec²(x) + tan²(x)]

Step-by-step explanation:

Remember your Trig derivatives.

Derivative of sec(x) is sec(x)tan(x)

Derivative of tan(x) = sec²(x)

Product Rule:

f'(x)g(x) + f(x)g'(x)

Step 1: Find 1st derivative of sec(x) (Trig Rule)

y' = sec(x)tan(x)

Step 2: Find 2nd derivative (Product Rule and Trig Rule)

y" = sec(x)sec²(x) + sec(x)tan(x)tan(x)

y" = sec³(x) + sec(x)tan²(x)

y" = sec(x) · [sec²(x) + tan²(x)]

The volume of the square-based pyramid is 3888 units³. Your answer is option B. 3888 units³.

The formula to calculate the volume of a pyramid is V = (1/3)Bh,

Where B is the area of the base and h is the height.

In this case, the base is a square with edge length 9 units, so the area is B = 9² = 81 units².

The height is given as 48 units.
Plugging these values into the formula, we get:
To find the volume of a square-based pyramid, you can use the following formula:

V = (1/3) * base area * height.

In this case, the base edge is 9 units and the height is 48 units.

First, find the base area:

A = side * side = 9 * 9

= 81 square units.

Next, calculate the volume:

V = (1/3) * 81 * 48 = 3888 cubic units.
V = (1/3)(81)(48)
V = 1296 units³
Therefore, the volume of the pyramid is 1296 units³, which is option b.

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Because all the coordinates of the vertices of square are positive so the square is present in the first quadrant.

If we are provided with any two points A(a,b) and B(c,d) in the co-ordinate plane then the distance between those two points can be calculated by using the distance formula that goes as,

D = √((d-b)²+(c-a)²)

Here, we provided with a square whose vertices are given to be L(1,1),I(1,6),F(6,1)and E(6,y).

We know that each side of the square is equal in length so we will find the length of the side LI and FE and then compare them with each other to find the missing coordinate y.

Now,

LI = √((1-1)²+(6-1)²)

LI = 5

FE = √((6-6)²+(y-1)²)

LI = FE

y-1 = 5

y = 6

As we can see that all the coordinates of the square are positive so the square will be lying in the first quadrant of the co-ordinate axis.

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A scientific hypothesis is a proposed explanation or prediction based on limited evidence or prior knowledge, which is subject to further investigation and testing.

A guess is a speculative, unsupported statement without any logical basis, whereas a hypothesis is an educated assumption derived from existing knowledge, observations, or theories. Unlike a guess, a hypothesis is testable and can be supported or refuted by evidence gathered through scientific methods.

Scientists need a hypothesis to provide a framework for their research and guide their investigations. It helps them define the specific question they want to answer and provides a starting point for designing experiments or making observations. By formulating a hypothesis, scientists can systematically evaluate and analyze data, ultimately leading to a deeper understanding of the phenomenon under investigation.

There are indeed scientific hypotheses that cannot be directly tested or proven due to practical or ethical constraints. For example, hypotheses related to historical events that occurred in the distant past may not have accessible evidence for direct testing. Additionally, some questions related to consciousness, subjective experiences, or philosophical concepts may lie beyond the scope of scientific inquiry, as they may not be objectively measurable or observable.

While science has its limitations, it is a powerful tool for investigating and understanding the natural world. However, there are questions that fall outside the realm of scientific inquiry and require other methods of investigation, such as philosophical or ethical considerations.

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Answer:

\(h(x)=2x^2-12x+9\),  \(p(x)=-5x^2-20x-5\)

Step-by-step explanation:

To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:

\(ax^2+bx+c\)

Where a, b, and c are constants.

Let's expand and simplify h(x).

\(2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9\)

Thus, \(h(x)=2x^2-12x+9\)

Let's do the same for p(x).

\(-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5\)

Thus, \(p(x)=-5x^2-20x-5\)

Answer:

What question do you need help with?

Step-by-step explanation:

Answer:

the next answers would be 16,18,20,22,24,26,28,30

Step-by-step explanation:

Answer:

The largest possible value of n is 11.

(A) is correct option.

Step-by-step explanation:

Given that,

The number with at least two digits,the last number was removed. The resulting number was n smaller than the previous one.

We need to find the largest possible value of n

Using given data,

The smallest number of two digit is 10.

Now, we removed last digit then we get 1 which is equal to 10 divided 10.

So, n = 10

But the largest number of two digit is 99.

We removed last digit then we get 9 which is equal to 99 divided 11.

So, n = 11

Hence, The largest possible value of n is 11.

(A) is correct option.

Answer:

1: 1

2: 1

3:2/5

4:1/4

The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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The value of (gof)(x) is (5x²-10)(x).

Here f(x) is given to us,

f(x) = x²-2

The value of g(x),

g(x) = 5x-8

Here we have to find a composite function, a composite function is a function in which two different functions are combined to form a third different function, in simple words we can understand it as a function inside a function

To find (gof)(x) means,    

We have to find, g(f(x))(x),

we have to put the value of f(x) in g(x) at the place of x.

Let us say that our final function is h(x),

h(x) = (gof)(x)

h(x) = g(f(x))(x)

h(x) = (5f(x)-8)(x)

h(x) = (5(x²-2))(x)

h(x) = (5x²-10)(x)

So, the value of (gof)(x) is (5x²-10)(x).

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Answer:

SP is Rs 800.

Step-by-step explanation:

MP = Rs 875

Discount = Rs 75

so

SP = MP - discount

= Rs 875 - Rs 75

= Rs 800

There are 87 fewer fish in small school compared to big school.

We solve addition and subtraction problems by focusing on either the action (joining or separating) or the relationship in the problem. Many problems involve monetary relationships.

This week, we looked at COMPARISON problems, which involve determining the similarities and differences between sets.

Difference Unknown: One type of compare problem entails determining how many more items are in one set than another. James, for example, has six mice. Joy has eleven mice. Joy has how many more mice than James?

Given,

Number of fish in small school = 25

Number of fish in big school =  112

then,

Number of fewer fish does small school have 112 -25 = 87

Thus, there are 87 fewer fish in school than big school.

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Answer:

$632.58

Step-by-step explanation:

It is given that Derek is paid a 6.5% commission (or 0.065 in decimals) on every appliance sold. It is also given that Derek sold $9,732.00 in total.

To solve, multiply the total sold with the commission percentage to find total amount of commission:

commission percentage x total sold = total amount of commission

Plug in the corresponding numbers to the corresponding variables. Let the variable, t, stand for the total amount of commissions:

0.065 x 9732 = t

t = 632.58

Derek's total commission is $632.58

~

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On the new planet, your mass will be the same. Therefore, the correct option is A.

The mass of an object is a fundamental property that remains constant regardless of the location or environment. Therefore, if you were to travel from Earth to a planet with an acceleration of gravity of 2.5 m/s², your mass would remain the same. Therefore, the correct answer is A: the same.

It is important to note that although the mass remains constant, the weight of the object may vary based on the strength of gravity. Weight is the measure of the force of gravity on an object, and it is directly proportional to the acceleration of gravity. As the acceleration of gravity increases, the weight of an object also increases.

Note: The question is incomplete. The complete question probably is: Suppose you go from the earth to a planet where the acceleration of gravity is 2.5 m/s. On the new planet, your mass will be about a. a) the same b. b) 7 times its value on Earth c. c) 2 times its value on Earth d. d) 4 times its value on Earth.

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Answer:

7g-13

Step-by-step explanation:

Answer:

-13 +17g

Step-by-step explanation:

−3 + 6g + 11g −10

-13 + 6g + 11g

-13 + 17g

Answer:

7.8

Step-by-step explanation:

The diameter is the full length across a circle. The radius is always half the diameter. if you divide 15.6 by 2 (to get half), we get 7.8. If this does not answer the question, let me know so I can edit

Answer:

1. Sine ratio of angle ∠C = 12/13

2. cos ratio for ∠C = 6/10

Step-by-step explanation:

1. sin = perpendicular /hypotuse

=> 12/13

2. cos = base / hypotuse

=> 6/10

ANSWER:

19.54

Step-by-step explanation:

23.7-8.3

=15.4

15.4+4.14

=18.54

Therefore, V is a subspace of R^n consisting of all symmetric matrices. Therefore, W is a subspace of R^n consisting of all matrices with trace 0.

(a) If V is the subspace of R^n consisting of all symmetric matrices, then V is a subspace because it satisfies the three conditions of a subspace:
- It contains the zero vector (the zero matrix is symmetric)
- It is closed under addition (the sum of two symmetric matrices is symmetric)
- It is closed under scalar multiplication (a scalar multiple of a symmetric matrix is symmetric)

To prove that V is a subspace, we can use the definition of a subspace and check that it satisfies the three conditions. Let A and B be two symmetric matrices in V and c be a scalar.
1. Zero vector: The zero matrix is symmetric, so it is in V.
2. Closed under addition: We need to show that A+B is symmetric.

Transpose of A+B = Transpose(A) + Transpose(B) (distributivity of transpose)
Transpose of A+B = A + B (because A and B are symmetric)
Therefore, A+B is symmetric, and it is in V.

3. Closed under scalar multiplication: We need to show that cA is symmetric.
Transpose of cA = cTranspose(A) (distributivity of transpose)
Transpose of cA = cA (because A is symmetric)
Therefore, cA is symmetric, and it is in V.

Therefore, V is a subspace of R^n consisting of all symmetric matrices.

(b) If W is the subspace of R^n consisting of all matrices with trace 0, then W is also a subspace because it satisfies the three conditions of a subspace:
- It contains the zero vector (the zero matrix has trace 0)
- It is closed under addition (the sum of two matrices with trace 0 has trace 0)
- It is closed under scalar multiplication (a scalar multiple of a matrix with trace 0 has trace 0)

To prove that W is a subspace, we can use the definition of a subspace and check that it satisfies the three conditions. Let A and B be two matrices with trace 0 in W and c be a scalar.
1. Zero vector: The zero matrix has trace 0, so it is in W.
2. Closed under addition: We need to show that A+B has trace 0.

Trace of A+B = Trace(A) + Trace(B) (linearity of trace)
Trace of A+B = 0 (because A and B have trace 0)
Therefore, A+B has trace 0, and it is in W.

3. Closed under scalar multiplication: We need to show that cA has trace 0.

Trace of cA = c*Trace(A) (linearity of trace)
Trace of cA = 0 (because A has trace 0)
Therefore, cA has trace 0, and it is in W.

Therefore, W is a subspace of R^n consisting of all matrices with trace 0.

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The probability of not getting a diamond card is \(\frac{4}{3}\).

There are four sets of cards in a standard deck: hearts, clubs, spades, and diamonds. There are thirteen cards in a suite: ace, 2, 3, 4, 5, 6, 7, 8, 9, jack, queen, and king are the remaining cards. Thus, there are 52 cards in total in the deck.

There are 52 possible outcomes in a deck of 52 cards. Since a deck of 52 cards contains 13 diamond cards, the total number of favorable outcomes in which it is not a diamond is 52 - 13=39.

As a result, the probability P of not receiving a diamond card is as follows:

\(p =\) \(\frac{53}{39}\) = \(\frac{3}{4}\)

Hence, the probability of not getting a diamond card is \(\frac{4}{3}\).

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​

Answer:

2r

Step-by-step explanation:

You suppose that the radius of a larger circle = r

so diameter = r*2 = 2r

aint really sure tho

Answer:

2R

Step-by-step explanation:

The formula to find the diameter states the relationship between the diameter and the radius. The diameter is made up of two segments that are each a radius. Therefore, the formula is: Diameter = 2 * the measurement of the radius. You can abbreviate this formula as d=2r.